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Volumn 138, Issue 4, 2010, Pages 1317-1331

Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials

Author keywords

Discrete Painlev equations; Orthogonal polynomials

Indexed keywords


EID: 77951467920     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-09-10152-1     Document Type: Article
Times cited : (48)

References (14)
  • 1
    • 0033241782 scopus 로고    scopus 로고
    • Algebraic entropy
    • MR1704282 (2000f:37040)
    • M. P. Bellon, C.-M. Viallet, Algebraic entropy, Commun. Math. Phys. 204 (1999), 425-437. MR1704282 (2000f:37040)
    • (1999) Commun. Math. Phys. , vol.204 , pp. 425-437
    • Bellon, M.P.1    Viallet, C.-M.2
  • 2
    • 43949127710 scopus 로고    scopus 로고
    • Ladder operators for q-orthogonal polynomials
    • MR2422628 (2009d:33021)
    • Y. Chen, M. Ismail, Ladder operators for q-orthogonal polynomials, J. Math. Anal. Appl. 345 (2008), 1-10. MR2422628 (2009d:33021)
    • (2008) J. Math. Anal. Appl. , vol.345 , pp. 1-10
    • Chen, Y.1    Ismail, M.2
  • 3
    • 0003362637 scopus 로고
    • An introduction to orthogonal polynomials
    • Gordon and Breach, New York, MR0481884 (58:1979)
    • T.S. Chihara, An Introduction to Orthogonal Polynomials, Mathematics and its Applications, 13, Gordon and Breach, New York, 1978. MR0481884 (58:1979)
    • (1978) Mathematics and Its Applications , vol.13
    • Chihara, T.S.1
  • 4
    • 0000533283 scopus 로고
    • Discrete Painlevé equations and their appearance in quantum gravity
    • MR1137067 (93a:58080)
    • A.S. Fokas, A.R. Its, A.V. Kitaev, Discrete Painlevé equations and their appearance in quantum gravity, Comm. Math. Phys. 142 (1991), 313-344. MR1137067 (93a:58080)
    • (1991) Comm. Math. Phys. , vol.142 , pp. 313-344
    • Fokas, A.S.1    Its, A.R.2    Kitaev, A.V.3
  • 5
    • 0000283311 scopus 로고
    • On the coefficients in the recursion formulae of orthogonal polynomials
    • MR0419895 (54:7913)
    • G. Freud, On the coefficients in the recursion formulae of orthogonal polynomials, Proc. Roy. Irish Acad. Sect. A 76(1) (1976), 1-6. MR0419895 (54:7913)
    • (1976) Proc. Roy. Irish Acad. Sect. , vol.A 76 , Issue.1 , pp. 1-6
    • Freud, G.1
  • 6
    • 12044253165 scopus 로고
    • Discrete versions of the Painlevé equations
    • MR1125951 (92j:39011)
    • B. Grammaticos, J. Hietarinta, A. Ramani, Discrete versions of the Painlevé equations, Phys. Rev. Lett. 67 (1991), 1829-1832. MR1125951 (92j:39011)
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 1829-1832
    • Grammaticos, B.1    Hietarinta, J.2    Ramani, A.3
  • 7
    • 0030164149 scopus 로고    scopus 로고
    • Discrete Painlevé equations: Coalescences
    • MR1399286 (97e:58131)
    • B. Grammaticos, A. Ramani, Discrete Painlevé equations: Coalescences, limits and degeneracies, Physica A 228 (1996), 160-171. MR1399286 (97e:58131)
    • (1996) Limits and Degeneracies, Physica , vol.A 228 , pp. 160-171
    • Grammaticos, B.1    Ramani, A.2
  • 8
    • 33847074584 scopus 로고    scopus 로고
    • Discrete Painlevé equations: A review
    • Springer, MR2087743 (2005g:39032)
    • B. Grammaticos, A. Ramani, Discrete Painlevé equations: A review, Lect. Notes Phys., 644, Springer, 2004, pp. 245-321. MR2087743 (2005g:39032)
    • (2004) Lect. Notes Phys. , vol.644 , pp. 245-321
    • Grammaticos, B.1    Ramani, A.2
  • 9
    • 0000758575 scopus 로고
    • Do integrable mappings have the Painlevé property?
    • MR1125950 (92f:58081)
    • B. Grammaticos, A. Ramani, V. Papageorgiou, Do integrable mappings have the Painlevé property?, Phys. Rev. Lett. 67 (1991), 1825-1828. MR1125950 (92f:58081)
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 1825-1828
    • Grammaticos, B.1    Ramani, A.2    Papageorgiou, V.3
  • 11
    • 33745311071 scopus 로고    scopus 로고
    • Freud's equations for orthogonal polynomials as discrete Painlevé equations,in symmetries and integrability of difference equations
    • (Canterbury, 1996), Cambridge University Press, MR1705232 (2000k:42036)
    • A.P. Magnus, Freud's equations for orthogonal polynomials as discrete Painlevé equations, in Symmetries and Integrability of Difference Equations (Canterbury, 1996), London Math. Soc. Lecture Note Ser., 255, Cambridge University Press, 1999, pp. 228-243. MR1705232 (2000k:42036)
    • (1999) London Math. Soc. Lecture Note Ser. , vol.255 , pp. 228-243
    • Magnus, A.P.1
  • 12
    • 51249164479 scopus 로고
    • On a q-deformation of the discrete Painlevé i equation and q-orthogonal polynomials
    • MR1271093 (95e:33024)
    • F. Nijhoff, On a q-deformation of the discrete Painlevé I equation and q-orthogonal polynomials, Lett. Math. Phys. 30 (1994), 327-336. MR1271093 (95e:33024)
    • (1994) Lett. Math. Phys. , vol.30 , pp. 327-336
    • Nijhoff, F.1
  • 13
    • 0034696720 scopus 로고    scopus 로고
    • Quadratic relations in continuous and discrete Painlevé equations
    • MR1766506 (2001d:34018)
    • A. Ramani, B. Grammaticos, T. Tamizhmani, Quadratic relations in continuous and discrete Painlevé equations, J. Phys. A. 33 (2000), 3033-3044. MR1766506 (2001d:34018)
    • (2000) J. Phys. A. , vol.33 , pp. 3033-3044
    • Ramani, A.1    Grammaticos, B.2    Tamizhmani, T.3
  • 14
    • 78650038496 scopus 로고    scopus 로고
    • Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials in "difference equations, special functions and orthogonal polynomials"
    • (S. Elaydi et al., eds.), MR2451211 (2009k:42055)
    • W. Van Assche, Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials, in "Difference Equations, Special Functions and Orthogonal Polynomials" (S. Elaydi et al., eds.), World Scientific, 2007, pp. 687-725. MR2451211 (2009k:42055)
    • (2007) World Scientific , pp. 687-725
    • Van Assche, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.